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We study ${T\overline{T}}$-like deformations of $d>2$ Yang-Mills theories. The standard ${T\overline{T}}$ flows lead to multi-trace Lagrangians, and the non-Abelian gauge structures make it challenging to find Lagrangians in a closed form. However, within the geometric approach to ${T\overline{T}}$, we obtain the closed-form solution to the metric flow and stress-energy tensor, and show that instanton solutions are undeformed. We also introduce new symmetrised single-trace ${T\overline{T}}$-like deformations, whose solutions in $d=4$ include the non-Abelian Born-Infeld Lagrangian proposed by Tseytlin in 1997., Comment: 9 pages

Assessment of proficiency of the learner is an essential part of Intelligent Tutoring Systems (ITS). We use Item Response Theory (IRT) in computer-aided language learning for assessment of student ability in two contexts: in test sessions, and in exercises during practice sessions. Exhaustive testing across a wide range of skills can provide a detailed picture of proficiency, but may be undesirable for a number of reasons. Therefore, we first aim to replace exhaustive tests with efficient but accurate adaptive tests. We use learner data collected from exhaustive tests under imperfect conditions, to train an IRT model to guide adaptive tests. Simulations and experiments with real learner data confirm that this approach is efficient and accurate. Second, we explore whether we can accurately estimate learner ability directly from the context of practice with exercises, without testing. We transform learner data collected from exercise sessions into a form that can be used for IRT modeling. This is done by linking the exercises to {\em linguistic constructs}; the constructs are then treated as "items" within IRT. We present results from large-scale studies with thousands of learners. Using teacher assessments of student ability as "ground truth," we compare the estimates obtained from tests vs. those from exercises. The experiments confirm that the IRT models can produce accurate ability estimation based on exercises.

This work reports an acoustic solidly mounted resonator (SMR) at 18.64 GHz, among the highest operating frequencies reported. The device is built in scandium aluminum nitride (ScAlN) on top of silicon dioxide (SiO2) and tantalum pentoxide (Ta2O5) Bragg reflectors on silicon (Si) wafer. The stack is analyzed with X-ray reflectivity (XRR) and high-resolution X-ray diffraction (HRXRD). The resonator shows a coupling coefficient (k2) of 2.0%, high series quality factor (Qs) of 156, shunt quality factor (Qp) of 142, and maximum Bode quality factor (Qmax) of 210. The third-order harmonics at 59.64 GHz is also observed with k2 around 0.6% and Q around 40. Upon further development, the reported acoustic resonator platform can enable various front-end signal-processing functions, e.g., filters and oscillators, at future frequency range 3 (FR3) bands., Comment: 5 pages, 9 figures, 5 tables

In this work, we study the duality symmetry group of Carrollian (nonlinear) electrodynamics and propose a family of Carrollian ModMax theories, which are invariant under Carrollian $\text{SO}(2)$ electromagnetic (EM) duality transformations and conformal transformation. We define the Carrollian $\text{SO}(2)$ EM transformations, with the help of Hodge duality in Carrollian geometry, then we rederive the Gaillard-Zumino consistency condition for EM duality of Carrollian nonlinear electrodynamics. Together with the traceless condition for the energy-momentum tensor, we are able to determine the Lagrangian of the Carrollian ModMax theories among pure electrodynamics. We furthermore study their behaviors under the $\sqrt{T\bar{T}}$ deformation flow, and show that these theories deform to each other and may reach two endpoints under the flow, with one of the endpoint being the Carrollian Maxwell theory. As a byproduct, we construct a family of two-dimensional Carrollian ModMax-like multiple scalar theories, which are closed under the $\sqrt{T\bar{T}}$ flow and may flow to a BMS free multi-scalar model., Comment: 39 pages, references added, major revised, results unchanged

This paper investigates what insights about linguistic features and what knowledge about the structure of natural language can be obtained from the encodings in transformer language models.In particular, we explore how BERT encodes the government relation between constituents in a sentence. We use several probing classifiers, and data from two morphologically rich languages. Our experiments show that information about government is encoded across all transformer layers, but predominantly in the early layers of the model. We find that, for both languages, a small number of attention heads encode enough information about the government relations to enable us to train a classifier capable of discovering new, previously unknown types of government, never seen in the training data. Currently, data is lacking for the research community working on grammatical constructions, and government in particular. We release the Government Bank -- a dataset defining the government relations for thousands of lemmas in the languages in our experiments.

The solution of Bethe ansatz equations for XXZ spin chain with the parameter $q$ being a root of unity is infamously subtle. In this work, we develop the rational $Q$-system for this case, which offers a systematic way to find all physical solutions of the Bethe ansatz equations at root of unity. The construction contains two parts. In the first part, we impose additional constraints to the rational $Q$-system. These constraints eliminate the so-called Fabricius-McCoy (FM) string solutions, yielding all primitive solutions. In the second part, we give a simple procedure to construct the descendant tower of any given primitive state. The primitive solutions together with their descendant towers constitute the complete Hilbert space. We test our proposal by extensive numerical checks and apply it to compute the torus partition function of the 6-vertex model at root of unity., Comment: 41 pages, 6 figures

We calculate the $T\bar{T}$-deformed entanglement entropy for integrable quantum field theories (IQFTs) using the form factor bootstrap approach. We solve the form factor bootstrap axioms for the branch-point twist fields and obtain the deformed form factors. Using these form factors, we compute the deformed von Neuman entropy up to two particle contributions. The solution of the form factor axioms is not unique. We find that for the simplest solution of the bootstrap axioms, the UV limit of the entanglement entropy takes the same form as the undeformed one, but the effective central charge is deformed. For solutions with additional CDD-like factors, we can have different behaviors. The IR corrections, which only depends on the particle spectrum is untouched., Comment: A miscalculation is corrected, conclusions are modified, references added

Electronic health record (EHR) data are increasingly used to support real-world evidence (RWE) studies. Yet its ability to generate reliable RWE is limited by the lack of readily available precise information on the timing of clinical events such as the onset time of heart failure. We propose a LAbel-efficienT incidenT phEnotyping (LATTE) algorithm to accurately annotate the timing of clinical events from longitudinal EHR data. By leveraging the pre-trained semantic embedding vectors from large-scale EHR data as prior knowledge, LATTE selects predictive EHR features in a concept re-weighting module by mining their relationship to the target event and compresses their information into longitudinal visit embeddings through a visit attention learning network. LATTE employs a recurrent neural network to capture the sequential dependency between the target event and visit embeddings before/after it. To improve label efficiency, LATTE constructs highly informative longitudinal silver-standard labels from large-scale unlabeled patients to perform unsupervised pre-training and semi-supervised joint training. Finally, LATTE enhances cross-site portability via contrastive representation learning. LATTE is evaluated on three analyses: the onset of type-2 diabetes, heart failure, and the onset and relapses of multiple sclerosis. We use various evaluation metrics present in the literature including the $ABC_{gain}$, the proportion of reduction in the area between the observed event indicator and the predicted cumulative incidences in reference to the prediction per incident prevalence. LATTE consistently achieves substantial improvement over benchmark methods such as SAMGEP and RETAIN in all settings., Comment: ERHs data

Language modeling is a fundamental task in natural language processing, which has been thoroughly explored with various architectures and hyperparameters. However, few studies focus on the effect of sub-word segmentation on the performance of language models (LMs). In this paper, we compare GPT and BERT models trained with the statistical segmentation algorithm BPE vs. two unsupervised algorithms for morphological segmentation -- Morfessor and StateMorph. We train the models for several languages -- including ones with very rich morphology -- and compare their performance with different segmentation algorithms, vocabulary sizes, and model sizes. The results show that training with morphological segmentation allows the LMs to: 1. achieve lower perplexity, 2. converge more efficiently in terms of training time, and 3. achieve equivalent or better evaluation scores on downstream tasks. Lastly, we show 4. that LMs of smaller size using morphological segmentation can perform comparably to models of larger size trained with BPE -- both in terms of (1) perplexity and (3) scores on downstream tasks. Points (2) and (4) impact on sustainability of LMs, since they reduce the model cost: size and computation time. While (2) reduces cost only in the training phase, (4) does so also in the inference phase., Comment: This submission published in EMNLP 2023

Bethe ansatz equations for spin-$s$ Heisenberg spin chain with $s\ge1$ are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra conditions for the Bethe roots to be physical and study the related completeness problem. In this paper, we propose the rational $Q$-system for the XXX$_s$ spin chain. Solutions of the proposed $Q$-system give all and only physical solutions of the Bethe ansatz equations required by completeness. This is checked numerically and proved rigorously. The rational $Q$-system is equivalent to the requirement that the solution and the corresponding dual solution of the $TQ$-relation are both polynomials, which we prove rigorously. Based on this analysis, we propose the extra conditions for solutions of the XXX$_s$ Bethe ansatz equations to be physical., Comment: typos corrected, some minor corrections

This paper presents the development of an AI-based language learning platform Revita. It is a freely available intelligent online tutor, developed to support learners of multiple languages, from low-intermediate to advanced levels. It has been in pilot use by hundreds of students at several universities, whose feedback and needs are shaping the development. One of the main emerging features of Revita is the introduction of a system of linguistic constructs as the representation of domain knowledge. The system of constructs is developed in close collaboration with experts in language teaching. Constructs define the types of exercises, the content of the feedback, and enable the detailed modeling and evaluation of learning progress.

While randomized controlled trials (RCTs) are the gold-standard for establishing the efficacy and safety of a medical treatment, real-world evidence (RWE) generated from real-world data (RWD) has been vital in post-approval monitoring and is being promoted for the regulatory process of experimental therapies. An emerging source of RWD is electronic health records (EHRs), which contain detailed information on patient care in both structured (e. g., diagnosis codes) and unstructured (e. g., clinical notes, images) form. Despite the granularity of the data available in EHRs, critical variables required to reliably assess the relationship between a treatment and clinical outcome can be challenging to extract. We provide an integrated data curation and modeling pipeline leveraging recent advances in natural language processing, computational phenotyping, modeling techniques with noisy data to address this fundamental challenge and accelerate the reliable use of EHRs for RWE, as well as the creation of digital twins. The proposed pipeline is highly automated for the task and includes guidance for deployment. Examples are also drawn from existing literature on EHR emulation of RCT and accompanied by our own studies with Mass General Brigham (MGB) EHR., Comment: 39 pages, 1 figure, 1 table

Deep learning methods have contributed substantially to the rapid advancement of medical image segmentation, the quality of which relies on the suitable design of loss functions. Popular loss functions, including the cross-entropy and dice losses, often fall short of boundary detection, thereby limiting high-resolution downstream applications such as automated diagnoses and procedures. We developed a novel loss function that is tailored to reflect the boundary information to enhance the boundary detection. As the contrast between segmentation and background regions along the classification boundary naturally induces heterogeneity over the pixels, we propose the piece-wise two-sample t-test augmented (PTA) loss that is infused with the statistical test for such heterogeneity. We demonstrate the improved boundary detection power of the PTA loss compared to benchmark losses without a t-test component.

We show that method of characteristics provides a powerful new point of view on $T\bar{T}$-and related deformations. Previously, the method of characteristics has been applied to $T\bar{T}$-deformation mainly to solve Burgers' equation, which governs the deformation of the \emph{quantum} spectrum. In the current work, we study \emph{classical} deformed quantities using this method and show that $T\bar{T}$ flow can be seen as a characteristic flow. Exploiting this point of view, we re-derive a number of important known results and obtain interesting new ones. We prove the equivalence between dynamical change of coordinates and the generalized light-cone gauge approaches to $T\bar{T}$-deformation. We find the deformed Lagrangians for a class of $T\bar{T}$-like deformations in higher dimensions and the $(T\bar{T})^{\alpha}$-deformation in 2d with generic $\alpha$, generalizing recent results in arXiv:2206.03415 and arXiv:2206.10515., Comment: 38 pages, 2 figures, references updated

Federated learning of causal estimands may greatly improve estimation efficiency by leveraging data from multiple study sites, but robustness to heterogeneity and model misspecifications is vital for ensuring validity. We develop a Federated Adaptive Causal Estimation (FACE) framework to incorporate heterogeneous data from multiple sites to provide treatment effect estimation and inference for a flexibly specified target population of interest. FACE accounts for site-level heterogeneity in the distribution of covariates through density ratio weighting. To safely incorporate source sites and avoid negative transfer, we introduce an adaptive weighting procedure via a penalized regression, which achieves both consistency and optimal efficiency. Our strategy is communication-efficient and privacy-preserving, allowing participating sites to share summary statistics only once with other sites. We conduct both theoretical and numerical evaluations of FACE and apply it to conduct a comparative effectiveness study of BNT162b2 (Pfizer) and mRNA-1273 (Moderna) vaccines on COVID-19 outcomes in U.S. veterans using electronic health records from five VA regional sites. We show that compared to traditional methods, FACE meaningfully increases the precision of treatment effect estimates, with reductions in standard errors ranging from $26\%$ to $67\%$., Comment: 59 pages

A notable challenge of leveraging Electronic Health Records (EHR) for treatment effect assessment is the lack of precise information on important clinical variables, including the treatment received and the response. Both treatment information and response often cannot be accurately captured by readily available EHR features and require labor intensive manual chart review to precisely annotate, which limits the number of available gold standard labels on these key variables. We consider average treatment effect (ATE) estimation under such a semi-supervised setting with a large number of unlabeled samples containing both confounders and imperfect EHR features for treatment and response. We derive the efficient influence function for ATE and use it to construct a semi-supervised multiple machine learning (SMMAL) estimator. We showcase that our SMMAL estimator is semi-parametric efficient with B-spline regression under low-dimensional smooth models. We develop the adaptive sparsity/model doubly robust estimation under high-dimensional logistic propensity score and outcome regression models. Results from simulation studies support the validity of our SMMAL method and its superiority over supervised benchmarks.

Large clinical datasets derived from insurance claims and electronic health record (EHR) systems are valuable sources for precision medicine research. These datasets can be used to develop models for personalized prediction of risk or treatment response. Efficiently deriving prediction models using real world data, however, faces practical and methodological challenges. Precise information on important clinical outcomes such as time to cancer progression are not readily available in these databases. The true clinical event times typically cannot be approximated well based on simple extracts of billing or procedure codes. Whereas, annotating event times manually is time and resource prohibitive. In this paper, we propose a two-step semi-supervised multi-modal automated time annotation (MATA) method leveraging multi-dimensional longitudinal EHR encounter records. In step I, we employ a functional principal component analysis approach to estimate the underlying intensity functions based on observed point processes from the unlabeled patients. In step II, we fit a penalized proportional odds model to the event time outcomes with features derived in step I in the labeled data where the non-parametric baseline function is approximated using B-splines. Under regularity conditions, the resulting estimator of the feature effect vector is shown as root-$n$ consistent. We demonstrate the superiority of our approach relative to existing approaches through simulations and a real data example on annotating lung cancer recurrence in an EHR cohort of lung cancer patients from Veteran Health Administration.

Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of the large Hessian matrix and its inverse. Iterative methods separately update parameters for finite dimensional component and infinite dimensional component have been developed to speed up single iteration, but they often take more steps until convergence or even sometimes sacrifice estimation precision due to sub-optimal update direction. We propose a computationally efficient implicit profiling algorithm that achieves simultaneously the fast iteration step in iterative methods and the optimal update direction in the Newton's method by profiling out the infinite dimensional component as the function of the finite dimensional component. We devise a first order approximation when the profiling function has no explicit analytical form. We show that our implicit profiling method always solve any local quadratic programming problem in two steps. In two numerical experiments under semiparametric transformation models and GARCH-M models, we demonstrated the computational efficiency and statistical precision of our implicit profiling method.

Risk modeling with EHR data is challenging due to a lack of direct observations on the disease outcome, and the high dimensionality of the candidate predictors. In this paper, we develop a surrogate assisted semi-supervised-learning (SAS) approach to risk modeling with high dimensional predictors, leveraging a large unlabeled data on candidate predictors and surrogates of outcome, as well as a small labeled data with annotated outcomes. The SAS procedure borrows information from surrogates along with candidate predictors to impute the unobserved outcomes via a sparse working imputation model with moment conditions to achieve robustness against mis-specification in the imputation model and a one-step bias correction to enable interval estimation for the predicted risk. We demonstrate that the SAS procedure provides valid inference for the predicted risk derived from a high dimensional working model, even when the underlying risk prediction model is dense and the risk model is mis-specified. We present an extensive simulation study to demonstrate the superiority of our SSL approach compared to existing supervised methods. We apply the method to derive genetic risk prediction of type-2 diabetes mellitus using a EHR biobank cohort.

Readily available proxies for time of disease onset such as time of the first diagnostic code can lead to substantial risk prediction error if performing analyses based on poor proxies. Due to the lack of detailed documentation and labor intensiveness of manual annotation, it is often only feasible to ascertain for a small subset the current status of the disease by a follow up time rather than the exact time. In this paper, we aim to develop risk prediction models for the onset time efficiently leveraging both a small number of labels on current status and a large number of unlabeled observations on imperfect proxies. Under a semiparametric transformation model for onset and a highly flexible measurement error models for proxy onset time, we propose the semisupervised risk prediction method by combining information from proxies and limited labels efficiently. From an initial estimator solely based on the labelled subset, we perform a one-step correction with the full data augmenting against a mean zero rank correlation score derived from the proxies. We establish the consistency and asymptotic normality of the proposed semi-supervised estimator and provide a resampling procedure for interval estimation. Simulation studies demonstrate that the proposed estimator performs well in finite sample. We illustrate the proposed estimator by developing a genetic risk prediction model for obesity using data from Partners Biobank Electronic Health Records (EHR).

In this work, we try to construct the Lax connections of $T\bar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $T\bar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way., Comment: 23 pages

In this paper, we present our study on the $T\bar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore we compute the exact energy spectrum of the deformed free theory by using the Brillouin-Wigner perturbation theory in an appropriate regularization scheme., Comment: 14 pages, 2 figures, references updated, more clarifications

A quantum integrability index was proposed in \cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \cite{GW} by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models ${SU(N)}/{SO(N)}$ and $SO(2N)/{SO(N)\times SO(N)}$. The indexes of these theories are all non-positive except for the case of ${SO(4)}/{SO(2)\times SO(2)}$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the $\mathbb{CP}^N$ model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well., Comment: 20 pages